A generalization of Roberts' counterexample to the fourteenth problem of Hilbert

DOI10.2748/tmj/1113246747zbMath1077.13003OpenAlexW1996573006WikidataQ124989325 ScholiaQ124989325MaRDI QIDQ1772206

Shigeru Kuroda

Publication date: 15 April 2005

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1113246747

zbMATH Keywords

Gröbner basesHilbert fourteenth problemnon-finitely generated algebra

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Actions of groups on commutative rings; invariant theory (13A50) Derivations and commutative rings (13N15) Commutative rings and modules of finite generation or presentation; number of generators (13E15) Group actions on affine varieties (14R20)

Related Items (10)

Linear counterexamples to the fourteenth problem of Hilbert ⋮ A counterexample to the fourteenth problem of Hilbert in dimension four ⋮ A simple proof of Nowicki's conjecture on the kernel of an elementary derivation ⋮ Hilbert's fourteenth problem and algebraic extensions ⋮ Hilbert's fourteenth problem and field modifications ⋮ Van den Essen's conjecture on the kernel of a derivation having a slice ⋮ A counterexample to the fourteenth problem of Hilbert in dimension three ⋮ A linear counterexample to the Fourteenth Problem of Hilbert in dimension eleven ⋮ Fields defined by locally nilpotent derivations and monomials ⋮ Invariants and separating morphisms for algebraic group actions

Cites Work

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• A counterexample to Hilbert's fourteenth problem in dimension 5
• A counterexample to Hilbert's fourteenth problem in dimension six
• Lectures on the fourteenth problem of Hilbert
• On some properties of elementary derivations in dimension six

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